I run 3 priests as my dps, it works out fine. I'm currently using a DK tank and a Pally main healer.

I am seriously contemplating bringing up my 4th priest (lv 69 now on the DK's account) and making her main heal and turning the pally into the main tank to make aoe healing a bit simpler. I'd say that it should definitely be viable as 4 priests + a pally for heroics, but i don't think you could keep all 4 as shadow all the time. Dropping in and out of shadowform is really expensive on mana and VE healing is waay underpowered for main tank healing in heroics.